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4. A simple random sample of 100 customers is selected from an account receivable portfolio and...

4. A simple random sample of 100 customers is selected from an account receivable portfolio and the sample mean account balance is $3000. The population standard deviation σ is known to be $300. ( 8 marks)
a. Construct a 90% confidence interval for the mean account balance of the population.
b. What is the margin of error for estimating the mean account balance at the 90% confidence level?
c. Construct a 90% confidence interval for the mean account balance of the population if the sample mean account balance is obtained from a random sample of 300 instead of 50.
d. Based on the results from a. and c., what can you say about the effect of a larger sample size on the length of the confidence interval at the same confidence level?
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